### Abstract

Agreement on a common time reference among the nodes is one of the most critical issues in the successful operation of the Wireless Sensor Networks (WSNs). In a previous paper [1], the Maximum Likelihood Estimator (MLE) for the clock offset of the silent nodes overhearing a two-way timing message exchange between two nodes, assuming an exponential link delay model, was obtained. This paper targets the derivation of Cramer-Rao Lower Bound (CRLB) for any unbiased clock offset estimator of the silent nodes as a performance threshold. The CRLB is shown to be inversely proportional to the square of the number of observations, and hence the variance of the MLE decreases very rapidly with the increase in data points. However, it is proved that the MLE does not achieve the CRLB and hence it is not efficient for small number of observations (although MLE has optimal properties for a large number of observations, i.e., it tends to become unbiased and attains CRLB). In addition, the CRLB for the clock offset estimator of the active node, as estimated by the silent node, is also derived and shown to be slightly better, but on a similar scale as the CRLB for the clock offset of the inactive node. copyright by EURASIP.

Original language | English |
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Journal | European Signal Processing Conference |

Publication status | Published - 2008 |

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### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering

### Cite this

**Cramer-Rao Lower Bound for the clock offset of silent nodes synchronizing through a general sender-receiver protocol in Wireless Sensornets.** / Chaudhari, Qasim M.; Serpedin, Erchin; Qaraqe, Khalid.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Cramer-Rao Lower Bound for the clock offset of silent nodes synchronizing through a general sender-receiver protocol in Wireless Sensornets

AU - Chaudhari, Qasim M.

AU - Serpedin, Erchin

AU - Qaraqe, Khalid

PY - 2008

Y1 - 2008

N2 - Agreement on a common time reference among the nodes is one of the most critical issues in the successful operation of the Wireless Sensor Networks (WSNs). In a previous paper [1], the Maximum Likelihood Estimator (MLE) for the clock offset of the silent nodes overhearing a two-way timing message exchange between two nodes, assuming an exponential link delay model, was obtained. This paper targets the derivation of Cramer-Rao Lower Bound (CRLB) for any unbiased clock offset estimator of the silent nodes as a performance threshold. The CRLB is shown to be inversely proportional to the square of the number of observations, and hence the variance of the MLE decreases very rapidly with the increase in data points. However, it is proved that the MLE does not achieve the CRLB and hence it is not efficient for small number of observations (although MLE has optimal properties for a large number of observations, i.e., it tends to become unbiased and attains CRLB). In addition, the CRLB for the clock offset estimator of the active node, as estimated by the silent node, is also derived and shown to be slightly better, but on a similar scale as the CRLB for the clock offset of the inactive node. copyright by EURASIP.

AB - Agreement on a common time reference among the nodes is one of the most critical issues in the successful operation of the Wireless Sensor Networks (WSNs). In a previous paper [1], the Maximum Likelihood Estimator (MLE) for the clock offset of the silent nodes overhearing a two-way timing message exchange between two nodes, assuming an exponential link delay model, was obtained. This paper targets the derivation of Cramer-Rao Lower Bound (CRLB) for any unbiased clock offset estimator of the silent nodes as a performance threshold. The CRLB is shown to be inversely proportional to the square of the number of observations, and hence the variance of the MLE decreases very rapidly with the increase in data points. However, it is proved that the MLE does not achieve the CRLB and hence it is not efficient for small number of observations (although MLE has optimal properties for a large number of observations, i.e., it tends to become unbiased and attains CRLB). In addition, the CRLB for the clock offset estimator of the active node, as estimated by the silent node, is also derived and shown to be slightly better, but on a similar scale as the CRLB for the clock offset of the inactive node. copyright by EURASIP.

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UR - http://www.scopus.com/inward/citedby.url?scp=84863763615&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84863763615

JO - European Signal Processing Conference

JF - European Signal Processing Conference

SN - 2219-5491

ER -